Large-Time Behavior for a Fully Nonlocal Heat Equation

We study the large-time behavior in all L p norms and in different space-time scales of solutions to a nonlocal heat equation in ℝ N involving a Caputo α -time derivative and a power of the Laplacian (−Δ) s , s ∈ (0,1), extending recent results by the authors for the case s = 1. The initial data are...

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Bibliographic Details
Published in:Vietnam journal of mathematics 2021-09, Vol.49 (3), p.831-844
Main Authors: Cortázar, Carmen, Quirós, Fernando, Wolanski, Noemí
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Norms
Original Article
Thermodynamics
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Summary:We study the large-time behavior in all L p norms and in different space-time scales of solutions to a nonlocal heat equation in ℝ N involving a Caputo α -time derivative and a power of the Laplacian (−Δ) s , s ∈ (0,1), extending recent results by the authors for the case s = 1. The initial data are assumed to be integrable, and, when required, to be also in L p . The main novelty with respect to the case s = 1 comes from the behaviour in fast scales, for which, thanks to the fat tails of the fundamental solution of the equation, we are able to give results that are not available neither for the case s = 1 nor, to our knowledge, for the standard heat equation, s = 1, α = 1.
ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-020-00452-w